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It can be shown that:

  • height = (d tan α tan β)/(tan α - tan β)
where:
  • α is the angle closest to the object
  • β is the angle further away from the object
  • d is the distance from the point of angle α to the point of angle β
Thus:

height = (53 ft × tan 31.4° × tan 26.4°)/(tan 31.4° - tan 26.4°) ≈ 140.87 ft

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Q: What is the height of a building if the angle of elevation to the top from a point on the ground is 31.4 degrees and from 53 feet further back it is 26.4 degrees?
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